Describe how flow limitation occurs at the equal pressure point and the role of dynamic airway compression in flow limitation.
6.
Define the components of work of breathing.
7.
Understand how dynamic compliance is different from static compliance and its contribution to work of breathing.
In this chapter, the principles that control air movement into and out of the lungs are examined. Dynamic mechanics is the study of physical systems in motion, and for the respiratory system it is the study of the properties of a lung whose volume is changing with time.
Air flows into and out of an airway when there is a pressure difference at the two ends of the airway. By way of review, during inspiration the diaphragm contracts, pleural pressure becomes more negative, and gas flows into the lung (see
Fig. 21.2 ). To meet the changing metabolic needs of the body, gas exchange depends on the speed at which fresh gas is brought to the alveoli and the rapidity with which the metabolic products of respiration (i.e., CO2) are removed. Two major factors determine the speed at which gas flows into the airways for a given pressure change: the pattern of gas flow and the resistance to airflow by the airways.
Patterns of Airflow
There are two major patterns of gas flow in the airways— laminar and turbulent. Laminar flow is parallel to the airway walls and is present at low flow rates. As the flow rate increases and particularly as the airways divide, the flow stream becomes unsteady and small eddies develop. At higher flow rates the flow stream is disorganized and turbulence occurs.
The pressure-flow characteristics of laminar flow were first described by the French physician Poiseuille and apply to both liquids and air. In straight circular tubes the flow rate (V̇ ) is defined by the following equation:
Equation 22.1 where P is the driving pressure, r is the radius of the tube, η is the viscosity of the fluid, and l is the length of the tube. It can be seen that driving pressure (P) is proportional to the flow rate (V̇ ); thus the greater the pressure, the greater the flow.
The flow resistance (R) across a set of tubes is defined as the change in driving pressure (ΔP) divided by the flow rate, or:
Equation 22.2
The units of resistance are cm H2O/L•sec. This equation is for laminar flow and demonstrates that the radius of the tube is the most important determinant of resistance. If the radius of the tube is reduced by half, the resistance will increase 16-fold. If, however, tube length is increased twofold, the resistance will increase only twofold. Thus the radius of the tube is the principal determinant of resistance. Stated another way, resistance is inversely proportional to the fourth power of the radius, and it is directly proportional to the length of the tube and to the viscosity of the gas.
In turbulent flow, gas movement occurs both parallel and perpendicular to the axis of the tube. Pressure is proportional to the flow rate squared. The viscosity of the gas increases with increasing gas density, and therefore the pressure drop increases for a given flow. Overall, gas velocity is blunted because energy is consumed in the process of generating eddies and chaotic movement. As a consequence, higher driving pressure is needed to support a given turbulent flow than to support a similar laminar flow.
Whether flow through a tube is laminar or turbulent depends on the Reynolds number. The Reynolds number (Re) is a dimensionless value that expresses the ratio of two dimensionally equivalent terms (kinematic/viscosity), as seen in the equation:
Equation 22.3 where d is the fluid density, v is the average velocity, r is the radius, and η is the viscosity. In straight tubes, turbulence occurs when the Reynolds number is greater than 2000. From this relationship it can be seen that turbulence is most likely to occur when the average velocity of the gas flow is high and the radius is large. In contrast, a low-density gas such as helium is less likely to cause turbulent flow. This is clinically relevant in states of increased airway resistance where a decrease in gas density (e.g., substituting helium for nitrogen in inspired air) can improve airflow.